221 research outputs found
Online Active Linear Regression via Thresholding
We consider the problem of online active learning to collect data for
regression modeling. Specifically, we consider a decision maker with a limited
experimentation budget who must efficiently learn an underlying linear
population model. Our main contribution is a novel threshold-based algorithm
for selection of most informative observations; we characterize its performance
and fundamental lower bounds. We extend the algorithm and its guarantees to
sparse linear regression in high-dimensional settings. Simulations suggest the
algorithm is remarkably robust: it provides significant benefits over passive
random sampling in real-world datasets that exhibit high nonlinearity and high
dimensionality --- significantly reducing both the mean and variance of the
squared error.Comment: Published in AAAI 201
Geometry of Power Flows and Optimization in Distribution Networks
We investigate the geometry of injection regions and its relationship to
optimization of power flows in tree networks. The injection region is the set
of all vectors of bus power injections that satisfy the network and operation
constraints. The geometrical object of interest is the set of Pareto-optimal
points of the injection region. If the voltage magnitudes are fixed, the
injection region of a tree network can be written as a linear transformation of
the product of two-bus injection regions, one for each line in the network.
Using this decomposition, we show that under the practical condition that the
angle difference across each line is not too large, the set of Pareto-optimal
points of the injection region remains unchanged by taking the convex hull.
Moreover, the resulting convexified optimal power flow problem can be
efficiently solved via }{ semi-definite programming or second order cone
relaxations. These results improve upon earlier works by removing the
assumptions on active power lower bounds. It is also shown that our practical
angle assumption guarantees two other properties: (i) the uniqueness of the
solution of the power flow problem, and (ii) the non-negativity of the
locational marginal prices. Partial results are presented for the case when the
voltage magnitudes are not fixed but can lie within certain bounds.Comment: To Appear in IEEE Transaction on Power System
An Unsupervised Deep Learning Approach for Scenario Forecasts
In this paper, we propose a novel scenario forecasts approach which can be
applied to a broad range of power system operations (e.g., wind, solar, load)
over various forecasts horizons and prediction intervals. This approach is
model-free and data-driven, producing a set of scenarios that represent
possible future behaviors based only on historical observations and point
forecasts. It first applies a newly-developed unsupervised deep learning
framework, the generative adversarial networks, to learn the intrinsic patterns
in historical renewable generation data. Then by solving an optimization
problem, we are able to quickly generate large number of realistic future
scenarios. The proposed method has been applied to a wind power generation and
forecasting dataset from national renewable energy laboratory. Simulation
results indicate our method is able to generate scenarios that capture spatial
and temporal correlations. Our code and simulation datasets are freely
available online.Comment: Accepted to Power Systems Computation Conference 2018 Code available
at https://github.com/chennnnnyize/Scenario-Forecasts-GA
- …